1. Little Mermaid

Copenhagen's most famous attraction is the bronze statue Hans Christian Anderson's beloved Little Mermaid character. She can be observed in her natural habitat lounging on a seaside rock all year round.

In August 2003, however, 90 women jumped into the strait of Øresund to form the number 90 (the anniversary year of her donation to the city of Copenhagen)—and they’ve been doing it ever since. Canal tours pass by the Little Mermaid daily.

2. Amalienborg Palace

Dating from the 1750s, the sprawling Amalienborg Palace is the winter home of the Danish royal family. For 45-70 DKK you can take a tour of two of the exquisite Rococo buildings. For some free entertainment, check out the changing of the guard that takes place every day at twelve noon.

The palace is open every day, except January-April and November-December, when it closes on Mondays.

3. National Gallery

General admission and tours are free at the National Gallery, home of some of the Western hemisphere's best artwork. The old meets the new at this unique museum, where funky, interactive exhibits like “create your own artwork” are regular features.

The museum is centrally located, near the main train stations, the Rosenborg Castle, and the Botanical Gardens. It's closed on Mondays.

4. Canal Tours

You shouldn't leave Copenhagen without going on a canal tour. Hour-long guided tours cruise by all of Copenhagen’s most famous attractions, including the National Museum, Amalienborg Palace, the Copenhagen Opera, and the Little Mermaid. For a cheaper experience, try the similarly-routed hop-on-hop-off waterbuses for about half the price.

5. Kronborg Castle

A breathtaking Renaissance palace, the Kronborg Castle, built by King Frederick II, also once served as a military fortress that guarded the Baltic Sea. As the historical home of Shakespeare’s Hamlet, Copenhagen’s Hamlet Festival takes place here every summer. In clear weather, you can see Sweden across the sound.

Like the Amalienborg Palace, Kronborg Castle is open every day for most of the year and closed Mondays in the spring and winter. And, depending on how much of the castle you want to see, adult ticket prices range from 30DKK to 90DKK (children 20DKK to 65DKK).

6. Tivoli Gardens

The world-famous Tivoli Gardens amusement park, located a few minutes' walk from City Hall Square, has been attracting thrill-seekers since 1874. Besides rides, the Gardens also feature concerts and dance performances, an aquarium, and over 30 restaurants. With all this stimulation, make sure you don’t miss the gardens themselves—hanging out here is a great way to relax after a long day of sightseeing (or rollercoaster riding).

Admission to the gardens is 95DKK (45DKK for children), but rides will cost you a few extra kroner. You can buy a multi-ride ticket for 205DKK.

7. National Museum

If you want to learn about Danish culture, head to the National Museum, located in the center of town on Frederiksholms Kanal. Housed in a Victorian mansion, this museum educates visitors on Danish history from prehistory to the present day.

Admission to the National Museum is free for most exhibits, as are the audio guides you can pick up at the door. Be sure to check the museum's website before visiting, as some parts of the museum are closed certain days in the summer and winter.

8. Strøget

If you’re looking for a place to splurge on a new designer handbag or outfit, Strøget is the place. As Copenhagen’s main shopping street, this central thoroughfare is also tourist central, with famous department stores like the Magasin du Nord.

But it’s worth a visit just to experience the elegance of the street’s high-end shops and street performers that have made Strøget famous. And if you’re looking for a bargain, you can find it here too: farther down the street are more affordable chains like Hennes & Mauritz.

9. Round Tower

Completed in 1642, the Round Tower is located in Copenhagen’s Latin Quarter, adjacent to St. Triniatis Church and not far from Strøget. In its early days it was used by scholars as an astronomical observatory, and it’s still a great place for a view of Copenhagen’s picturesque rooftops and winding lanes.

Admission is 25 DKK, but the view is worth the price. And best of all, there are no stairs—just a long, winding ramp. The tower is open daily except Christmas and New Year's.

10. Viking Ship Museum

Scenic Roskilde, a few miles west of Copenhagen, is the home of the fascinating Viking Ship Museum. Five reconstructed ships discovered in the 1960s are the main feature of the museum, but there’s also an educational center and archeological workshops on the neighboring artificial island.

The museum is open daily except on winter holidays, so if you want to save some cash, try visiting the Viking Ship Museum in the off season, when tickets are about half price.